Combination of n things taken k at a time?

5!'s cancel, 9x8x7x6=3024 combinations, yeah yeah yeah....but I don't understand this other permutation thing for the life of me.

What's canceling, what's doing what? They don't explain, give explicit solution, thus how am I supposed to learn? The book doesn't even give explicit solution. Math always does this to me...anyways...:

You can see I am completely missing out on this concept. I probably messed up either by canceling out 12!'s when I wasn't supposed to or by diving by 11---I probably should have done something with the 11!, but I didn't. I randomly dropped the exclamation point, but I really don't know what to do, so that's probably why i dropped the exclamation point.

Hopefully my problem is explicit now. =[

p.s. the solution was a textbook solution, not a solution that I made, which is why I am questioning it.